As is known, traditional incandescent lamps are provided with a tungsten (W) filament which is made incandescent by the passage of electric current. The efficiency of traditional incandescent lamps is limited by Planck's law, which describes the spectral intensity I(λ) of the radiation emitted by the tungsten filament of the lamp at the equilibrium temperature T, and by heat losses through conduction and convection. The energy irradiated by the tungsten filament in the visible range of the electromagnetic spectrum is proportional to the integral of the curve I(λ) between λ1=380 nm and λ2=780 nm, and is at the most equal to 5-7% of the total energy.
According to Kirchoff's law, under thermal equilibrium conditions the electromagnetic radiation absorbed by a body at a specific wavelength is equal to the electromagnetic radiation emitted. A direct consequence of this law is that the spectral emittance “ε” of a surface coincides with spectral absorbance “α”. Spectral absorbance “α” in turn is linked to spectral reflectance “ρ” and to spectral transmittance “τ” through the relationship α=1−τ−ρ whence descends the relationship l−ε=τ+ρ. For an opaque material, τ is substantially nil and spectral reflectance ρ coincides with (l−ε); note, however, that any material, for sufficiently small thickness values, has a spectral transmittance τ different from 0.
The relationship τ+ρ=l−ε implicitly states that, if the surface of an opaque body has a low spectral reflectance at a given wavelength, the corresponding spectral emissivity will be very high; vice versa, if spectral reflectance is high, the corresponding emissivity will be low.
Emissivity, absorbance, transmittance and reflectance are functions, not only of wavelength, but also of temperature T and of the angle of incidence/emission θ, but the above relationships hold true for any T, any wavelength and any angle, since they descend from pure thermodynamic considerations. In general, the relationship τ+ρ=l−ε can thus be rewritten asτ(λ,T, θ)+ρ(λ, T, θ)=l−ε(λ, T, θ).
The curves of reflectance and spectral transmittance at a given temperature T, from which descend the values of absorbance and emissivity at that temperature, can be calculated a priori through the optical constants (always at temperature T) of the material or of the materials constituting the emitter for any geometry of the emitter and for any angle of incidence/emission.
The optical constants of the material are the real value n and the imaginary value k of the refraction index; the values of n and k for most known materials have been measured experimentally and are available in the literature. In general, there are no values of n and k available at the temperatures of interest for incandescent sources. The reflectance and transmittance calculation, presented in the remainder of the description and in the related figures, refer to optical constants measured at ambient temperature; however, the above considerations have general validity and can easily be transferred to the case of high temperatures.
In a traditional incandescent source, radiation is emitted by a tungsten filament, whose operating temperature is around 2800K; the emitted radiation follows the law of the black body, whose corresponding spectrum is given by Planck's relationship. The filament can be considered, with good approximation, a grey body, i.e. with constant emissivity throughout the spectrum of interest. By definition, a black body is a grey body with emissivity ε(λ, T, θ) independent of λ and of θ and equal to 100% (maximum value). The emission spectrum of a grey body can be obtained multiplying the black body spectrum I(λ) (given by Planck's relationship) for an emissivity value of ε(T) For a non-grey body, Planck's curve Planck I(λ) must instead be multiplied times a spectral emissivity curve ε(λ, T, θ).
The spectral emissivity of tungsten is generally a function of temperature; it has been demonstrated empirically that the mean emissivity of tungsten follows the relationshipεm(T)=−0.0434+1.8524*10−4*T−1.954*10−8*T2.
At low temperatures the spectral emissivity curve can easily be derived measuring the reflectance spectrum of tungsten and applying the relationship ε(λ, T, θ)=1−ρ(λ, T, θ); at incandescence temperatures, this type of measure becomes unfeasible, because the spectrum of reflectance and the spectrum of emission are obviously mixed.
At the temperature of 2800K, the mean emissivity of tungsten is about 30%, which corresponds to a mean reflectance of about 70%. At 2800K, the peak in the emission spectrum is at a wavelength slightly greater than 1 micron, which presupposes that most of the radiation is emitted in the form of infrared.
In particular for a grey body at a temperature of 2800K, slightly less than 10% of radiation is emitted in the visible spectrum (380-780 nm), whilst over 20% is emitted in near infrared (780-1100 nm).
In fact, the tungsten filament is not an actual grey body, but it has a spectral emissivity that is more or less constant in the visible spectrum, and tends significantly to decrease in near infrared, as is readily apparent from the reflectance and spectral emissivity curves shown in FIG. 1. In the graph of FIG. 1, the curves CRW and CEW respectively represent the reflectance and the emissivity of tungsten at ambient temperature for different wavelengths in the visible and near infrared spectrum.
This causes the efficiency of a tungsten filament, i.e. the ratio between visible radiation and total emitted radiation, is far greater than that of a grey body; the advantage is still more significant when considering the spectral emissivity at ambient temperature. FIG. 2 compares the Planck's curve at 2800K, designated CP, with the spectral power emitted by a tungsten filament at 2800K; for tungsten, the chart shows both the experimentally measured values (curve PM), and the values calculated using the optical constants of tungsten at ambient temperature (curve PC).
According to U.S. Pat. No. 4,196,368, the efficiency of a light bulb can be improved by modifying the surface micro-structure of an incandescent filament, so as to increase emissivity in the visible region of the spectrum and/or suppress the emission of energy outside the visible region of the spectrum; a similar solution is also disclosed by DE-A-198 45 423.
Another way suggested in U.S. Pat. No. 4,196,368 for improving efficiency is to coat the filament with a thin refractory material, to suppress filament evaporation. Similarly, in order to prevent or reduce blackening of a lamp envelope due to evaporation of material from the filament of an incandescent lamp, GB-A-2 032 173 suggests coating the filament with a refractory or ceramic material.